In this work, we focus on the characterisation of the vertical structure of velocity moments across the Galactic disk. The K-type giants are a kind of long-lived objects with high luminosities. The large sample size and the wide spatial coverage of the observed K giants make them feasible tracers for the Galactic kinematics. We sample the K giants from the catalog of LAMOST DR8, which contains observations from October 24, 2011 to May 27, 2020. The K giants are selected based on the surface gravities (\(\rm {log}\emph {g}\) ) and effective temperatures (\(T_{\rm {eff}}\) ) measured by the LAMOST team. The selection criteria follow the conditions given by [1]} such that \(4000\,\rm {K}<T_{\rm {eff}}<4600\,\rm {K}\)  with \(\rm {log}\emph {g}<3.5\)  and \(4600\,\rm {K}<T_{\rm {eff}}<5600\,\rm {K}\)  with \(\rm {log}\emph {g}<4\) . We obtain the metallicities (\(\rm {[Fe/H]}\) ) and the line-of-sight velocities (\(v_{\rm {los}}\) ) from the LAMOST data. We reject stars with \(\rm {[Fe/H]}\leqslant -1\)  to exclude likely halo stars. It has been noted that there exists a systematic offset in the measured \(v_{\rm {los}}\)  of around \(5-7\mathrm {km\,s}^{-1}\)  ([2]}; [3]}; [4]}; [5]}; [6]}), which needs to be added to \(v_{\rm {los}}\) . We select stars from the LAMOST sample that also have measurements of line-of-sight velocities in the Gaia data to determine the offset. The Gaia EDR3 contains line-of-sight velocities for more than 7 million sources ([7]}, [8]}), with systematic bias at a level of \(0.1\,\mathrm {km\,s}^{-1}\)  [9]}. We use the Gaia line-of-sight velocities satisfying \(\rm {RV_{-}NB_{-}TRANSITS}>5\)  as calibrators, and find that the offset in the LAMOST measurement is \(5.34\,\mathrm {km\,s}^{-1}\)  (see Fig. 1).
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